# Long-range interactions of kinks

@article{Christov2019LongrangeIO,
title={Long-range interactions of kinks},
author={Ivan C. Christov and Robert J. Decker and A Demirkaya and Vakhid A. Gani and Panayotis G. Kevrekidis and Roman V. Radomskiy},
journal={Physical Review D},
year={2019}
}
• Published 8 October 2018
• Mathematics
• Physical Review D
We present a computational analysis of the long-range interactions of solitary waves in higher-order field theories. Our vehicle of choice is the $\varphi^8$ field theory, although we explore similar issues in example $\varphi^{10}$ and $\varphi^{12}$ models. In particular, we discuss the fundamental differences between the latter higher-order models and the standard $\varphi^4$ model. Upon establishing the power-law asymptotics of the model's solutions' approach towards one of the steady…

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## References

SHOWING 1-10 OF 84 REFERENCES
Intersoliton forces in weak-coupling quantum field theories
We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional
Kink-Antikink Collisions in the φ4 Equation: The n-Bounce Resonance and the Separatrix Map
• Physics
SIAM J. Appl. Dyn. Syst.
• 2005
A detailed mathematical explanation of a phenomenon known as the two-bounce resonance observed in collisions between kink and antikink traveling waves of the $\phi^4$ equations of mathematical physics, including the origin of several mathematical assumptions needed by previous researchers are provided.
Kink-Antikink Scattering in \phi^4 and \phi^6 Models
For kink-antikink scattering within the \phi^4 non--linear field theory in one space and one time dimension resonance type configurations emerge when the relative velocity between kink and antikink
Kink dynamics in a parametric ϕ6 system: a model with controllably many internal modes
• Physics
• 2017
A bstractWe explore a variant of the ϕ6 model originally proposed in Phys. Rev.D 12 (1975) 1606 as a prototypical, so-called, “bag” model in which domain walls play the role of quarks within hadrons.
Kink interactions in the (1+1)-dimensional $\phi^6$ model
• Physics
• 2014
We study kink scattering processes in the ( 1 + 1 ) -dimensional φ 6 model in the framework of the collective coordinate approximation. We find critical values of the initial velocities of the
Higher-order field theories: $φ^6$, $φ^8$ and beyond
• Physics
• 2018
The φ model has been the “workhorse” of the classical Ginzburg– Landau phenomenological theory of phase transitions and, furthermore, the foundation for a large amount of the now-classical
Kink-Antikink Collisions in the Two-Dimensional φ4 Model
Inelastic kink-antikink collisions are investigated in the two-dimensional ¢' model. It is shown that a bound state of the kink and antikink is formed when the colliding velocity V is less than a
Scattering of the double sine-Gordon kinks
• Materials Science
• 2017
We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity $$v_{{\mathrm {cr}}}$$vcr of the colliding kinks, which separates
Fractal structure in the scalar λ ( φ 2 − 1 ) 2 theory
• Physics
• 1991
Head-on collisions of kink and antikink solitons are investigated numerically in the classical one-dimensional λ(Φ 2 -1) 2 model. It is shown that whether a kink-antikink interaction settles to a